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The numerical treatment is significantly simpler if the molecule cannot dissociate. Then, one can expand the wave function in a set of suitable square-integrable basis functions and derive a set of first-order differential equations. If the basis functions are simple and if the potential energy surface has a simple coordinate dependence, several modes of a polyatomic molecule can be treated (see, for example, Ref
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The numerical treatment is significantly simpler if the molecule cannot dissociate. Then, one can expand the wave function in a set of suitable square-integrable basis functions and derive a set of first-order differential equations. If the basis functions are simple and if the potential energy surface has a simple coordinate dependence, several modes of a polyatomic molecule can be treated (see, for example, Ref. 5 and references therein).
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Since the bound-state wave functions exponentially decay into the classically forbidden region, they are never really zero except at the boundary of the grid. As a consequence, the unit matrix in (Formula presented) has a tiny distortion and also the nondiagonal elements are not exactly zero. However, these deviations from the ideal are negligibly small
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Since the bound-state wave functions exponentially decay into the classically forbidden region, they are never really zero except at the boundary of the grid. As a consequence, the unit matrix in (Formula presented) has a tiny distortion and also the nondiagonal elements are not exactly zero. However, these deviations from the ideal are negligibly small.
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